A053725
Number of n X n binary matrices of order dividing 3 (also number of solutions to X^3=I in GL(n,2)).
Original entry on oeis.org
1, 3, 57, 1233, 75393, 19109889, 6326835201, 6388287561729, 23576681450405889, 120906321631678693377, 1968421511613895105052673, 111055505036706392268074909697, 8965464105556083354144035638870017
Offset: 1
- V. Jovovic, The cycle index polynomials of some classical groups, Belgrade, 1995, unpublished.
-
\\ See Morison theorem 2.6
\\ F(n,q,k) is number of solutions to X^k=I in GL(i, GF(q)) for i=1..n.
\\ q is power of prime and gcd(q, k) = 1.
B(n,q,e)={sum(m=0, n\e, x^(m*e)/prod(k=0, m-1, q^(m*e)-q^(k*e)))}
F(n,q,k)={if(gcd(q,k)<>1, error("no can do")); my(D=ffgen(q)^0); my(f=factor(D*(x^k-1))); my(p=prod(i=1, #f~, (B(n, q, poldegree(f[i,1])) + O(x*x^n))^f[i,2])); my(r=B(n,q,1)); vector(n, i, polcoeff(p, i)/polcoeff(r, i))}
F(10, 2, 3) \\ Andrew Howroyd, Jul 09 2018
A063393
Number of solutions of x^10=1 in general affine group AGL(n,2).
Original entry on oeis.org
2, 10, 92, 23200, 21391520, 35841831040, 95709758320640, 6206883395497062400, 1502803598296957497344000, 654083813715060854940290252800, 450433384822340709737677746549555200
Offset: 1
A063385
Number of solutions of x^2=1 in general affine group AGL(n,2).
Original entry on oeis.org
2, 10, 92, 1696, 59552, 4124800, 556101632, 148425895936, 78099471368192, 81705857229783040, 169694608681978560512, 702657511446831375056896, 5797142351555426979908943872, 95500953266115919784543392890880, 3140561514292519005433439594146168832
Offset: 1
A063386
Number of solutions of x^3=1 in general affine group AGL(n,2).
Original entry on oeis.org
1, 9, 225, 6273, 968193, 307091457, 144510377985, 338450286215169, 1535613392752345089, 11693653105154832465921, 423384155808298738368118785, 29155340360444250715547947237377
Offset: 1
A063387
Number of solutions of x^4=1 in general affine group AGL(n,2).
Original entry on oeis.org
2, 16, 512, 45376, 8556032, 4883562496, 8980929708032, 42613515533418496, 486724235988568113152, 16895428758428581359517696, 1832013338159753885910032187392, 514041193283459103260028716172967936
Offset: 1
A063388
Number of solutions of x^5=1 in general affine group AGL(n,2).
Original entry on oeis.org
1, 1, 1, 21505, 10665985, 3583770625, 1040317415425, 22653952038273025, 2926557495587739009025, 255470267616151345324621825, 19124940736236376955275154817025, 1747866583310404907502405460766490625
Offset: 1
A063389
Number of solutions of x^6=1 in general affine group AGL(n,2).
Original entry on oeis.org
2, 18, 540, 75168, 35803296, 52295889024, 165440621998080, 1667054559389773824, 57054517078704967876608, 7229212455140774474869112832, 3089828410800189940613202019614720
Offset: 1
A063390
Number of solutions of x^7=1 in general affine group AGL(n,2).
Original entry on oeis.org
1, 1, 385, 46081, 3809281, 27335393281, 219971402072065, 1196544590358773761, 34605327838407410319361, 15221801372279275206853263361, 5309386094113063403935896849874945
Offset: 1
A063391
Number of solutions of x^8=1 in general affine group AGL(n,2).
Original entry on oeis.org
2, 16, 512, 65536, 33554432, 68719476736, 562949953421312, 13098680304497852416, 668820864146264243044352, 107256832111726994824496152576, 61528102027124002571478755339927552
Offset: 1
A063392
Number of solutions of x^9=1 in general affine group AGL(n,2).
Original entry on oeis.org
1, 9, 225, 6273, 968193, 20785780737, 166595296845825, 8149768955751661569, 951855018651756891865089, 115831656001165053232244326401, 75552701461152667657380793652609025
Offset: 1
Showing 1-10 of 12 results.